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, 72 (11), 2276-2291

History Is Written by the Victors: The Effect of the Push of the Past on the Fossil Record

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History Is Written by the Victors: The Effect of the Push of the Past on the Fossil Record

Graham E Budd et al. Evolution.

Abstract

Survivorship biases can generate remarkable apparent rate heterogeneities through time in otherwise homogeneous birth-death models of phylogenies. They are a potential explanation for many striking patterns seen in the fossil record and molecular phylogenies. One such bias is the "push of the past": clades that survived a substantial length of time are likely to have experienced a high rate of early diversification. This creates the illusion of a secular rate slow-down through time that is, rather, a reversion to the mean. An extra effect increasing early rates of lineage generation is also seen in large clades. These biases are important but relatively neglected influences on many aspects of diversification patterns in the fossil record and elsewhere, such as diversification spikes after mass extinctions and at the origins of clades; they also influence rates of fossilization, changes in rates of phenotypic evolution and even molecular clocks. These inevitable features of surviving and/or large clades should thus not be generalized to the diversification process as a whole without additional study of small and extinct clades, and raise questions about many of the traditional explanations of the patterns seen in the fossil record.

Keywords: Crown groups; diversification rates; mass extinctions; molecular clocks; push of the past; survivorship bias.

Figures

Figure 1
Figure 1
An example diversification with 10,000 living species, an extinction rate of 0.5 per species per million years and a diversification time of 500 Myrs. The implied speciation rate is 0.5107 per species per million years and thus the underlying diversification rate is 0.0107 per species per million years. (A) Diversity plot through time. As in all other figures, the blue line is the number of species at time t and the red line the number of species that will give rise to living species. Shading gives 95% confidence areas. Note large POTPa and POTPr. (B) Observed diversification rate at beginning of diversification (note scale of 100 Myrs). (C) Implied diversification rate correlation with diversity generated by this distribution.
Figure 2
Figure 2
(A) Illustration of the rate of plesion creation along the surviving lineages (black solid line) and the mean number of plesions created along each stem group (red dashed line) through time. As rate of plesion creation is almost flat for most of the time, it follows that the decline in number of plesions per stem group depends on the stem groups decreasing in size temporally. (B) Observed diversification rate (red) and probability density functions of the first crown group (black, solid) and origin times for pairs of random living species (black, dashed) against time. All plots for a diversification over 500 Myrs in total, nT=10,000, λ=0.51, and μ=0.5 (i.e., the same example as Fig. 1). Note the likely emergence of the first crown group as the POTPa decays.
Figure 3
Figure 3
A small section of a tree at a time distant from the present. Red branches represent lineages that survived until the present, and where they diverge represents the birth of a new crown group. Green branches represent plesions that do not survive until the present. As per the results presented herein and in Stadler and Steel (2012), the stem lineages species generate plesions at a rate close to 2λ and the plesions themselves speciate at rate λ: the crown groups form at rate λμ.
Figure 4
Figure 4
Patterns of diversification and stem‐ and crown‐group formation for different (constant) diversification parameters. For each column T = 500 Myrs and nT=1000. All rates given per species per million years. Shading gives 95% confidence areas. Row one gives plots of diversity and diversity that gives rise to extant species through time; row two gives observed average diversification rates through time over the first 100 Myrs (i.e., the POTPa effect); row three gives probability density function plots for the appearance of the first crown group (red) and for crown groups defined by random pairs of living species. (A–C) Yule process with μ=0 and λ=0.014. (D–F) low μ net diversification with μ=0.1 and λ=0.109. (G–I) high μ net diversification with μ=0.5 and λ=0.505. For the second column, median clade survival time is 10.5 Myrs and 8.2% of clades would survive 500 Myrs; for column 3, the corresponding numbers are 2 Myrs and 1%. Note different time scale on second row.
Figure 5
Figure 5
The impact of number of remaining species on a postextinction POTPa on a clade that had diversified for 250 Myrs to generate 1000 species, assuming clade survival to the present, with baseline diversification λμ=0.01. The curves from bottom to top represent background extinction rates of μ= 0 (Yule process), 0.1, 0.3, and 0.5 per species per million years.
Figure 6
Figure 6
Expected observed initial diversification rate as a function of clade survival time for different values of underlying extinction rate, μ in a neutral model. As μ increases, a bigger and bigger POTPa is required to ensure the clade survives the first few million years.
Figure 7
Figure 7
(A) Diversification when an exceptionally large clade is generated with the parameters of Figure 1 (here, 10 x larger than expected). An early lineage effect is introduced as this is where fluctuation in actual rates is most likely. (B) Calculated decline of lineage rate (thus in red) through time. Note that it lasts considerably longer than the POTPa although is of smaller effect (here initially c. 10 x the background rate of λμ). (C) Implied lineage diversification rate correlation with lineage diversity generated by this distribution. The dashed line in (B) and (C) indicates the expected background rate (0.01) in each case.

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